1. Field of the Invention
The invention relates in general to a computation apparatus and computation therefor, and more particularly to a computation apparatus and non-linear computations therefor.
2. Description of the Related Art
Liquid crystal displays (LCDs) have been commonly used because of the merit of being thin, light, and having low radiation. Although the LCDs with higher resolutions and display frequencies are being developed, the displays suffer from a bottleneck in responding to voltages applied between liquid crystal layer of the displays. FIG. 1A illustrates this bottleneck in terms of a timing diagram of gray-levels of liquid crystal molecules (LC) when an input voltage is applied to the liquid crystal molecules. FIG. 1B shows a timing diagram of the input voltages. When an input voltage of V1 is applied to the LC, the gray-level of the LC has a value of L1. When an input voltage of V2 is applied to the LC, the gray-level of the LC has a value of L2.
The response of the LC does not keep pace with the change in the input voltage applied. Referring to FIGS. 1A and 1B, when the input voltage changes at time t1 from V1 to V2, the gray-level of the LC changes from L1 to L2. Due to the characteristics of the LC, the transition of the gray-level from L1 to L2 occurs from time t1 to t3, as indicated by a curve C1 in FIG. 1A. From time t4 to t6, the input voltage changes from V2 to V1 so that the gray-level of the LC decreases from L2 to L1, as indicated by a curve C3 in FIG. 1A. However, when the changes in the input voltage become more rapid, as in a display with higher display frequencies and resolutions, the response of the LC will be failed to keep pace with the changes due to the characteristics of the LCD, resulting in a residual effect in displaying frames on the LCD. In order to avoid the residual effect, a method of overdrive has been proposed. At time t1, an overdrive input voltage of V2′, instead of the input voltage of V2, is initially employed for driving the LC so that the change of the gray-level from L1 to L2 takes a smaller period from time t1 to t2, as indicated by a curve C2 in FIG. 1A. When the gray-level reaches L2, the voltage applied to the LC is switched from the overdrive input voltage of V2′ to the input voltage of V2. Similarly, at time t4, an overdrive input voltage of V1′, instead of the input voltage of V1, is initially employed for driving the LC so that the change of the gray-level from L2 to L1 takes a smaller period from time t4 to t5, as indicated by a curve C4 in FIG. 1A. When the gray-level reaches L1, the voltage applied to the LC is switched from the overdrive input voltage of V1′ to the input voltage of V1.
When the overdrive voltages of V1′ and V2′ are employed for driving the LC, the corresponding overdrive gray-level values can be recorded and associated with respective previous gray-level values and current gray-level values to establish an overdrive lookup table. In the lookup table, the previous gray-level values and the current gray-level values are regarded as two kinds of index values, denoted by PF and CF, respectively, and are associated with the corresponding overdrive gray-level values, denoted by OD. An overdrive gray-level value OD can then be determined according to the overdrive lookup table. For example, the previous gray-level index values PF and the current gray-level index values CF for 256 gray-levels result in an overdrive lookup table having 256 by 256 pieces of data for overdrive gray-level values OD. Since such a lookup table has a large amount of data, an overdrive lookup table of a reduced amount of data, for example, 17 by 17, is then derived to reduce the size of an overdrive data generator that includes the overdrive lookup table. FIG. 2 illustrates an overdrive lookup table of 17 by 17.
With a reduced-sized overdrive lookup table, interpolation is additionally required for determining overdrive gray-level values that cannot be directly obtained from the lookup table. FIGS. 3A, 3B, and 3C show three cases that require interpolation. FIG. 3A shows a first case where the previous gray-level index values PF in the overdrive lookup table contain no item matching previous gray-level data PD. For example, the current gray-level data CD and previous gray-level data PD are 64 and 180 respectively. Since the previous gray-level index values PF has no value of 180, interpolation is required for determination of a corresponding overdrive gray-level value A1 of the data CD and PD to drive the LC. FIG. 3B shows a second case where the current gray-level index values CF in the overdrive lookup table contain no item matching current gray-level data CD. For example, the current gray-level data CD and previous gray-level data PD are 70 and 176 respectively. Since the current gray-level index values CF has no value of 70, interpolation is required for determination of a corresponding overdrive gray-level value A2 of the data CD and PD to drive the LC.
In the third case shown in FIG. 3C, both previous gray-level data PD and current gray-level data CD have no corresponding items found in the previous gray-level index values PF and the current gray-level index values CF in the overdrive lookup table. For example, the current gray-level data CD and previous gray-level data PD are 70 and 180 respectively. Since the current gray-level index values CF has no value of 70 and the previous gray-level index values PF has no value of 180, interpolation is required for determination of corresponding overdrive gray-level values A1 and A3 of the data PD and then a desired overdrive gray-level value A4 according to the values A1 and A3 so as to drive the LC with the desired overdrive gray-level value A4.
FIG. 4 illustrates a conventional interpolator. The interpolator 400 includes a subtractor 401, a subtractor 402, a multiplier 403, a shifter 404, and an addition/subtraction device 405. For the first or second case where the gray-level index values F contain no item matching gray-level data D, the subtractor 401 is applied with overdrive gray-level values OD1 and OD2 that respectively correspond to gray-level index values F1 and F2 which come closest to the gray-level data D. The subtractor 401 performs subtraction of the overdrive gray-level values OD1 and OD2 and outputs the difference Q1. The subtractor 402 receives the gray-level data D and the gray-level index value F1, performs subtraction of them, and outputs the difference Q2. The multiplier 403 receives the differences Q1 and Q2 and outputs the production Q3. The shifter 404 receives the production Q3, divides it by 16, and output a result Q4 indicating the integer quotient of the division. The addition/subtraction device 405 receives the result Q4 and the overdrive gray-level value OD1, and outputs an overdrive gray-level value On for driving the LC. For the third case, three times of similar interpolation are required. For the sake of brevity, the third case will not be described in detail. Finally, the interpolator 400 in FIG. 4 achieves a conventional interpolation that can be expressed by: On=OD1±(OD1−OD2)*(D−F1)/(F1−F2).
However, the conventional interpolation obtains the overdrive gray-level value On by linear computations. Such interpolation requires a number of multiplication and addition operations, and the multipliers, notably, are complicated, time-consuming, and large-sized computation devices so that it is difficult to meet the requirement of high computation performance and compact size in implementation. Besides, the results of linear interpolation may not be the closest overdrive gray-level values as determined by experiments.